A couple of days ago, Markus posted Eb/N0 numbers for WSPR and OPERA,
for comparison to the BPSK VLF tests (see below).
Some may be interested in a table with Eb/N0 values for some more amateur
modes, which I composed some weeks ago for an article in the Dutch amateur
radio magazine 'Electron':
Needed SNR Net datarate Needed
Mode in 2500 Hz in bits/s Eb/N0 Comments
SSB voice +10 dB 20 +31 dB very
rough estimate
CW (ZRO-test, by ear) -18 dB 0.54 +16 dB based on
avg.pwr; peak 3 dB higher
CW (QRSS-3, waterfall) -26 dB 0.13 +14 dB same
CW (RSCW software, 12 wpm) -12 dB 4 +13 dB same
OPERA-2 -23 dB 0.23 +14 dB peak
pwr. 3 dB higher; 2 dB lower if counting CRC-bits as information
RTTY -5 dB 32 +14 dB
PSK31 -10 dB 31 +9 dB
WSPR -29 dB 0.45 +5 dB not
counting energy in sync bits; otherwise 3 dB higher
WSPR-15 -38 dB 0.056 +5 dB same
JT65 (for EME) -24 dB 1.54 +5 dB same
Coherent BPSK on VLF -57 dB 0.0058 -1 dB
Theoretical limit -1.59 dB
(The table is formatted for display using a fixed-width font.)
I have to emphasize that the SNR and Eb/N0 values should be taken with a
grain of salt, especially for the modes that do not use heavy FEC, since
those don't have a no sharp threshold.
The SNR values quoted come from a variety of sources on the web, and the
BPSK/VLF line is based on Markus and Paul's experiments from last May
(obviously, since I created the table before the recent experiments by Dex
and Paul).
73, Pieter-Tjerk, PA3FWM
On Sun, Jan 04, 2015 at 04:11:22PM +0100, Markus Vester wrote:
> [....]
>
> The ultimate goal of this work has been to take decoding sensitivity close to
> the theroretical limit. An universal metric for this is Eb/N0, the ratio of
> the
> received signal energy per payload bit (Eb in Joules) and the noise spectral
> power density (N0 in Watt/Hertz, equivalent to "noise energy" in Joules). The
> Shannon limit for long messages spread to infinite bandwidth is
> Eb/N0 = ln(2) = -1.59 dB,
> which (similar to the speed of light) cannot be surpassed by any possible
> encoding scheme. Paul's and Dex' experiments showed that his codes can come
> within about a dB of this limit in a real long-distance propagation
> experiment.
>
> To put that into perspective, let's derive Eb/N0 figures for two popular
> digital modes:
>
> WSPR-15 transmits 50 information bits in 15 minutes, ie one bit in 18 seconds.
> The decoding threshold is -38 dB in 2.5 kHz, or -4 dBHz. This gives
> Eb/N0 = 10 log(18) - 4 dB = +8.5 dB,
> ie. about 10 dB above the Shannon limit. Note that although different speed
> variants (eg WSPR-2) need different power, the minimum energy per bit has to
> remain the same.
>
> Opera-32 carries 28 information bits in 32.6 minutes, ie. one bit in 70
> seconds. The threshold is about -39.5 dB in 2.5 kHz, (-5.5 dBHz), referenced
> to
> the average power of the 50% dutycycle on-off keying. This gives
> Eb/N0 = 10 log(70) - 5.5 dB = +13 dB
> or about 14.5 dB above Shannon. Note however that for LF / VLF transmissions,
> the limit will often be antenna voltage and peak power rather than average
> power, which can result in a further 3 dB disadvantage for Opera against
> frequency- or phase-modulated techniques.
>
> The opds correlation decoder can go about 9 dB lower than Opera. But of course
> it can only find the best match from an a-priori defined list of callsigns,
> and
> doesn't attempt to decode any message.
>
> However we must recognize that the amateur modes spend a significant part of
> their energy to provide a reference for synchronisation, so not all of the Eb/
> N0 difference is due to less efficient encoding. The "nude" FEC-PSK mode
> doesn't contain any such overhead. So it can only work when the link has a
> stable phase (like on VLF), and the decoder has been given accurate
> information
> on carrier frequency and symbol timing.
>
> All the best,
> Markus (DF6NM)
>
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